sometimes the riders can be very unaware of their own safe riding.
I couldn't agree more, there is almost nothing as ignorant as horse riders who do not appear to be aware of the traffic around them.
I think they they must also drive large shiny 4 x 4's or people carriers when not horse riding.... but that's another subject.
Like you I also drive a lot with my work, around 35,000 miles a year, and unless the road is narrow, when single file for bike and horse is preferable, I really can't see how single file is any different to side by side. Let me put it another way, what's easier to overtake, a slow moving car or a tractor towing a small machine.
For what it's worth, when we get traffic behind us, we tend to ride the horses single file, as it cuts out a lot of the verbal abuse, but I still think it's as broad as it's long... literally.
"Try not to punch any clowns"